Given that ABCD is a rhombus with angle A equal to 60 degrees, OE equal to 2√2, and BD equal to 4, we can find AE by using trigonometry.

Since ABCD is a rhombus, all sides are equal in length. Therefore, AB is also equal to 4.

We can use trigonometry to find AE. Since angle A is 60 degrees, angle B is also 60 degrees. Thus, triangle ABE is an equilateral triangle, and angle ABE is 60 degrees.

We can find AE using the sine rule in triangle ABO:

sin(60 degrees) = OE / AB
sin(60 degrees) = 2√2 / 4
sin(60 degrees) = √3 / 2

From this, we can find AE:

AE = sin(60 degrees) AB
AE = (√3 / 2) 4
AE = 2√3

Therefore, AE is equal to 2√3.